Transcript Atomic Systems and Bonding

: Atomic Systems and
Bonding :
R. R. Lindeke, Ph.D.
ME 2105– Lecture Series 2
ISSUES TO ADDRESS...
 The Structure of Matter
 A Quick Review from chemistry
 What Promotes Bonding?
 What type of Bonding is Possible?
 What Properties are Inferred from
Bonding?
Just as before:
How the atoms are arranged
& how they bond
GREATLY AFFECTS
Their FINAL PROPERTIES
& therefore use
ATOMIC Structure
Primary & secondary
Electron configurations
BONDING
Structure of Matter:
 Atoms are the smallest particle in Nature that exhibits
the characteristics of a substance

The radius of a typical atom is on the order of 0.
0.0000000001 meter and cannot be studied without very
powerful microscopes
Pictured here is an
“Electron
Microscope” It can
greatly magnify
materials but can’t
resolve individual
atom – we need a
TEM or STP for that
Structure of Matter: A molecule consists of
2 or more atoms bound together
In a common glass of water “upon
closer examination” we would find
a huge number of Water
“Molecules” consisting of 1 atom of
Oxygen and 2 atoms of hydrogen
Atomic Structure (Freshman Chem.)
 atom –
electrons – 9.11 x 10-31 kg (.000911x 10-27 kg)
protons
-27 kg
1.67
x
10
neutrons
}
 atomic number = # of protons in nucleus of atom
= # of electrons of neutral species
 A [=] atomic mass unit = amu = 1/12 mass of
12C
Atomic wt = wt of 6.023 x 1023 molecules or atoms
1 amu/atom = 1g/mol
C
H
12.011
1.008 etc.
Atomic Weight is rarely a whole number
– it is a weighted average of all of the
natural isotopes of an “Element”
What is this in weight or mass in
“Real Terms”
 Example 1:
What is this in weight or mass in “Real Terms”
Structure of Matter – an Element
 Any material that is composed of only one type of
atom is called a chemical element, a basic element, or
just an element.
 Every element has a unique atomic structure.
 Scientists know of only about 109 basic elements at
this time. (This number has a habit of changing!)
 All matter is composed of combinations of one or
more of these elements.
 Ninety-one of these basic elements occur naturally on
or in the Earth (Hydrogen to Uraninum).
 These elements are pictured in the “Periodic Table”
The Periodic Table of the Elements
Structure of Matter
 Each of the “boxes” in the
periodic table help us to
understand the details of a
given elements
 Here we see atomic
Number (# of Electrons or
Protons) and Atomic
Weight
 Some tables provide
information about an
elements “Valance State”
or the ability to gain or
shed their outermost
electrons when they form
molecules or “Compounds”
Structure of Matter
 These outermost or Valence electrons
determine all of the following
properties concerning an element:
1)Chemical
2)Electrical
3)Thermal
4)Optical
Schematic Image of Atoms:
Atomic
number
is 29
Electronic Structure
 Electrons have wavelike and particulate
properties.
 This means that electrons exist in orbitals defined by
a probability. – Boer coupled w/ Schrödinger models
 Each orbital is located at a discrete energy level
determined by quantum numbers.
Quantum #
Designation
n = principal (energy level/shell) K, L, M, N, O (1, 2, 3, etc.)
l = subsidiary (orbitals)
s, p, d, f (0, 1, 2, 3,…, n -1)
ml = magnetic
1(s), 3(p), 5(d), 7(f)
ms = spin
½, -½
Electron Energy States
• have discrete energy states
Electrons • tend to occupy lowest available energy state.
4d
4p
N-shell n = 4
Can hold up to
32 electrons
3p
3s
M-shell n = 3
Can hold up to
18 Electrons
2p
2s
L-shell n = 2
Can hold up to 8
electrons
1s
K-shell n = 1
Can hold up to 2
electrons
3d
4s
Energy
Adapted from Fig. 2.4,
Callister 7e.
More exhaustively:
SURVEY OF ELEMENTS
• For Most elements: This Electron configuration not stable.
Element
Atomic #
Hydrogen
1
Helium
2
Lithium
3
Beryllium
4
Boron
5
Carbon
6
...
Neon
10
Sodium
11
Magnesium
12
Aluminum
13
...
Electron configuration
1s 1
1s 2
(stable)
1s 2 2s 1
1s 2 2s 2
1s 2 2s 2 2p 1
1s 2 2s 2 2p 2
...
Argon
...
Krypton
1s 2 2s 2 2p 6 3s 2 3p 6
(stable)
...
1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)
•
18
...
36
1s 2 2s 2 2p 6
(stable)
1s 2 2s 2 2p 6 3s 1
1s 2 2s 2 2p 6 3s 2
1s 2 2s 2 2p 6 3s 2 3p 1
...
Why? Valence (outer) shell usually not filled completely so the
electrons can ‘move out’!
Lets Try one: Here we have Iron
‘Fe’ (w/ Atomic Number 26)
ex: Fe - atomic # =
4d
4p
1s2 2s2 2p6 3s2 3p6 3d 6 4s2
N-shell n = 4
3d
4s
Energy
3p
3s
M-shell n = 3
2p
2s
L-shell n = 2
1s
K-shell n = 1
Electron Configurations
 Valence electrons – those in unfilled shells
 Filled shells are more stable
 Valence electrons are most available for
bonding and tend to control the chemical
properties
 example:
1s2
C (atomic number = 6)
2s2 2p2
valence electrons
H
accept 2e
accept 1e
inert gases
give up 1e
give up 2e
give up 3e
Matter (or elements) Bond as a
result of their Valance states
He
Li Be
O
F Ne
Na Mg
S
Cl Ar
K Ca Sc
Rb Sr
Y
Cs Ba
Se Br Kr
Te
I
Xe
Po At Rn
Fr Ra
Electropositive elements:
Readily give up electrons to become
+ ions.
Electronegative elements:
Readily acquire electrons
to become - ions.
Molecular/Elemental Bonding
 Bonding is the result of the balance of the
force of attraction and the force of repulsion
of the electric nature of atoms (ions)
 Net Force between atoms: FN = FA + FR and
at some equilibrium (stable) bond location of
separation, FN = 0 or FA = FR
 From Physics we like to talk about bonding
energy where:
r
E   Fdr   Fdr

Equilibrium
separation (r0) is
about .3 nm for
many atoms
Bonding Energy
 Energy – minimum energy most stable
 Energy balance of attractive and repulsive
terms
EN = EA + ER =
-
A
r
-
B
rn
Repulsive energy ER
Interatomic separation r
Net energy EN
Attractive energy EA
n is 7-9
for most
ionic
pairs
Here: A, B and n are “material
constants”
EN = EA + ER =
r
r


-
A
r
-
B
rn
EN   FN dr    FA  FR  dr
r
E A   FA dr  - A

r
where :
A
1
4 0
 Z1e  Z 2e 
-- Coulomb's Law
Z i is valence number of the species,
e is electronic charge,
 0 is the permittivity of a vacuum (8.85x10-12 F / m)
Figure 2.7 Net bonding force curve for a Na+−Cl−
pair showing an equilibrium bond length of a0 =
0.28 nm.
Bonding Energy, the Curve Shape,
and Bonding Type
 Properties depend on shape, bonding type and values
of curves: they vary for different materials.
 Bonding energy (minimum on curve) is the energy
that would be required to separate the two
atoms to an infinite separation.
 Modulus of elasticity depends on energy (force)
versus distance curve: the slope at r = r0 position on
the curve will be quite steep for very stiff materials,
slopes are shallower for more flexible materials.
 Coefficient of thermal expansion depends on E0 versus
r0 curve: a deep and narrow trough correlates with a
low coefficient of thermal expansion
Bonding Types of Interest:
 Ionic Bonding: Based on donation and acceptance of
valance electrons between elements to create strong
“ions” – CaIONs and AnIONs due to large electronegativity differences
 Covalent Bonding: Based on the ‘sharing’ of valance
electrons due to small electro negativity differences
 Metallic Bonding: All free electrons act as a moving
‘cloud’ or ‘sea’ to keep charged ion cores from flying
apart in their ‘stable’ structure
 secondary bonding: van der wahl’s attractive forces
between molecules (with + to – ‘ends’)
 This system of attraction takes place without valance
electron participation in the whole
 Valence Electrons participate in the bonding to build
the molecules not in ‘gluing’ the molecules together
Ionic bond – metal
donates
electrons
+
nonmetal
accepts
electrons
Dissimilar electronegativities
ex: MgO
Mg
1s2 2s2 2p6 3s2
[Ne] 3s2
Mg2+ 1s2 2s2 2p6
[Ne]
O
1s2 2s2 2p4
O2- 1s2 2s2 2p6
[Ne]
Note: after exchange we have a stable (albeit ionic) electron structure for
both Mg & O!
Examples: Ionic Bonding
• Predominant bonding in Ceramics
NaCl
MgO
CaF 2
CsCl
Give up electrons
Acquire electrons
Ionic Bonding – a Closely held Structure of
+Ions and –Ions (after this Valence
exchange)




These structure a held together
by Coulombic Bonding forces
after the Atoms exchange
Valance Electrons to form the
stable ionic cores:
It the solid state these ionic cores
will sit at highly structured
“Crystallographic Sites”
We can compute the coulombic
forces holding the ions together –
it is a balance between attraction
force (energy) due to the ionic
charge and repulsion force
(energy) due to the nuclear cores
of the ions
These forces of attraction and
repulsion compete and will
achieve a energy minimum at
some inter-ion spacing
Figure 2.10
Formation of an ionic
bond note effect of
ionization on atomic
radius. The cation (Na+)
becomes smaller than the
neutral atom, while the
anion (Cl−) becomes
larger than the neutral
atom
Example: Using these energy
issues
We seek FA (the force is a derivative of E A )
 
A
dE A d r
A  Z e  Z 2e 
FA 

 2  1
dr
dr
r0
4 0  r0 2

 0.1602 x10-18 
4  3.14159  8.854 x10
-12
2
   0.098  0.181 x10

-9 2
 FA  compute it
where:
1
A
 Z1e  Z 2e  which is Coulomb's Law
4 0
Here, ‘r0’ equals the sum of the ionic radii of each and
represents the r in the energy balance equations!
Another Example (working
backward with Coulomb’s Law):
We seek r0
FA  given 
A
1
4 0
 r   A   Z e  Z e 
d A
dr
1
r0
2
2
4 0  r0 2
 Z1e  Z 2e  -- Coulomb's Law
  Z1e  Z 2e   2
-10
 r0  (rS -2  rMg 2 )  
  2.489 x10 m
 4 0  FA 
and just solve for rMg 2 after plug & Chug  0.065 nm
1
The largest number of ions of radius R that can coordinate
an atom of radius r is 3 when the radius ratio r/R = 0.2.
(Note: The instability for CN = 4 can be reduced, but not
eliminated, by allowing a three-dimensional, rather than a
coplanar, stacking of the larger ions.) – to keep the ionic
characteristic in balance!
The minimum radius ratio, r/R, that can produce
threefold coordination is 0.155
Covalent Bonding
 similar electronegativity  share electrons
 bonds determined by valence – s & p orbitals
dominate bonding
 Example: CH4
shared electrons
H
from carbon atom
C: has 4 valence e-,
CH 4
needs 4 more
H: has 1 valence e-,
needs 1 more
Electronegativities
are comparable.
H
C
H
H
shared electrons
from hydrogen
atoms
Adapted from Fig. 2.10, Callister 7e.
Three-dimensional
structure of bonding in
the covalent solid,
carbon (diamond). Each
carbon atom (C) has
four covalent bonds to
four other carbon
atoms. Note, the bondline schematic of
covalent bonding is
given a perspective view
to emphasize the spatial
arrangement of bonded
carbon atoms.
Tetrahedral configuration of covalent bonds with
carbon. The bond angle is 109.5°.
During Polymerization, We
break up one “double
bond” (must supply 162
kcal/mole) and add two
single bonds (releases
2*88 = 176 kcal/mole)
which requires a catalyst
to start but will be selfsustaining (releasing
heat!) once the process
begins
“Electro-negativity” Values for determining
Ionic vs. Covalent Bond Character
Give up electrons
Acquire electrons
Primary Bonding
Ionic-Covalent Mixed Bonding

(X A -X B )2 


4
% ionic character = 1- e
 x (100 %)




where XA & XB are ‘Pauling’ electronegativities
Ex: MgO
 1.2
XMg =
XO = 3.5

%IonicCharacter  1 - e

- 3.5-1.2
2
4

 100%  73.4%

Metallic Bonding:
In a metallic
bonded material,
the valence
electrons are
“shared” among all
of the ionic cores
in the structure not
just with nearest
neighbors!
Considering Copper:






It valance electrons are far from the nucleus and
thus are not too tightly bound (making it easier to
‘move out’)
outside shell had only one electron
When the valence electron in any atom gains
sufficient energy from some outside force, it can
break away from the parent atom and become
what is called a free electron
Atoms with few electrons in their valence shell
tend to have more free electrons since these
valence electrons are more loosely bound to the
nucleus. In some materials like copper, the
electrons are so loosely held by the atom and so
close to the neighboring atoms that it is difficult to
determine which electron belongs to which atom!
Under normal conditions the movement of the
electrons is truly random, meaning they are
moving in all directions by the same amount.
However, if some outside force acts upon the
material, this flow of electrons can be directed
through materials and this flow is called
electrical current in a conductor.
SECONDARY BONDING
Arises from interaction between “electric” dipoles
• Fluctuating dipoles
ex: liquid H 2
H2
H2
asymmetric electron
clouds
+
-
+
secondary
bonding
-
H H
H H
secondary
bonding
Adapted from Fig. 2.13, Callister 7e.
• Permanent dipoles-molecule induced
-general case:
-ex: liquid HCl
-ex: polymer
+
-
H Cl
secondary
bonding
+
secondary
bonding
H Cl
Adapted from Fig. 2.14,
Callister 7e.
secondary bonding
Summary: Bonding
Comments
Type
Bond Energy
Ionic
Large!
Nondirectional (ceramics)
Covalent
Variable
large-Diamond
small-Bismuth
Directional
(semiconductors, ceramics
polymer chains)
Metallic
Variable
large-Tungsten
small-Mercury
Nondirectional (metals)
Secondary
smallest
Directional
inter-chain (polymer)
inter-molecular
Properties From Bonding: Tm
• Melting Temperature, Tm
Energy
• Bond length, r
r
• Bond energy, Eo
ro
Energy
r ounstretched length
r
Eo =
“bond energy”
smaller Tm
r
larger Tm
Tm is larger if Eo is larger.
Properties From Bonding : a
• Coefficient of thermal expansion, a
length, L o
unheated, T1
DL
coeff. thermal expansion
heated, T2
DL
= a(T2 -T1)
Lo
• a ~ symmetry at ro
Energy
unstretched length
ro
E
o
E
o
smaller a
larger a
r
a is larger if Eo is smaller.
Summary: Primary Bonds
Ceramics
(Ionic & covalent bonding):
Metals
(Metallic bonding):
Polymers
(Covalent & Secondary):
Large bond energy
large Tm
large E
small a
Variable bond energy
moderate Tm
moderate E
moderate a
Directional Properties
Secondary bonding dominates
small Tm
small E
large a